Recipients of the 2011 Clay Research Awards announced

The 2011 Clay Research Awards will be presented: to Yves Benoist
(CNRS, Université de Paris Sud 11) and Jean-François Quint (CNRS
Université de Paris 13) for their work on stationary measures and orbit
closures; and to Jonathan Pila (Mathematical Institute, Oxford) for his resolution
of the André-Oort Conjecture in the case of products of modular curves.

The award ceremony will take place at the 2011 Clay Research Conference,
to be held May 16-17 at Harvard University in Science Center Lecture Hall A.
Benoist, Pila, and Quint will speak on their work at that occasion.

CITATIONS

Yves Benoist and Jean-François Quint

For their spectacular work on stationary measures and orbit
closures for actions of non-abelian groups on homogeneous spaces. This
work is a major breakthrough in homogeneous dynamics and related areas
of mathematics. In particular, Benoist and Quint proved the following conjecture
of Furstenberg. Let H be a Zariski dense semisimple subgroup of a Lie
group which acts by left translations on the quotient of G by a
discrete subgroup with finite covolume. Consider a probability
measure m on H whose support generates H. Then any
m-stationary probability measure for such an action is H-invariant.

Jonathan Pila:

For his resolution of the Andre-Oort Conjecture in the case
of products of modular curves. This work gives the first unconditional proof
of fundamental cases of these general conjectures
beyond the original theorem of André concerning the product of two
such curves. The foundational techniques that Pila developed to achieve this
breakthrough range from results in real analytic geometry which give
sharp upper bounds for the number of rational points of bounded height
on certain analytic sets, to the use of O-minimal structures in
mathematical logic.

Provided by The Clay Mathematics Institute